Unrecognized function or variable 'x'.

Hello.

I don’t understand why I don’t have x defined after running the code, if initially it says errors. Help me please

function  F=M36(x)
F=[3*x(1)*x(2) - x(1)^2 - x(2)^2 - 5; 
   7*x(1)^2 * x(2)^2 - x(1)^4 - x(2)^4 - 155];
options = optimoptions('fsolve','Display','iter');
[~,~] = fsolve(F,[-4,0],options);
[~,~] = fsolve(F,[0,4],options);
disp('Plotting graphs of the left sides of the system equations:')
x=-5:0.1:5; 
y= (3/2).*x+ sqrt((13/4).*x.^2+5); 
plot(y,x,'b')
hold on
x=-5:0.1:5; 
y = sqrt((x^4 + 155) / (7*x^2 - y^2)); 
plot(y,x,'b')
hold on
grid on
legend('Graphic solution');
end

[Dyuman Joshi]

It's not clear to me what you want to do.

However, I have cleaned some things up in the code, check it out -

M36

                                             Norm of      First-order   Trust-region
 Iteration  Func-count     ||f(x)||^2           step       optimality         radius
     0          3              169362                        1.05e+05              1
     1          6             55891.4              1         2.56e+04              1
     2          9             29320.3              1         5.51e+03              1
     3         12             24368.2              1              633              1
     4         15             24050.7              1             6.04              1
     5         18               23882              1              387              1
     6         21             2418.33            2.5            6e+03            2.5
     7         24             1421.97        5.08058         1.33e+04           6.25
     8         27             46.4093       0.628623         1.54e+03           6.25
     9         30            0.202455      0.0731741             99.1           6.25
    10         33         5.13304e-07     0.00327403            0.158           6.25
    11         36          4.6714e-17    9.04034e-06          1.5e-06           6.25
    12         39                   0    5.10498e-11                0           6.25

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


                                             Norm of      First-order   Trust-region
 Iteration  Func-count     ||f(x)||^2           step       optimality         radius
     0          3              169362                        1.05e+05              1
     1          6             55891.4              1         2.56e+04              1
     2          9             29320.3              1         5.51e+03              1
     3         12             24368.2              1              633              1
     4         15             24050.7              1             6.04              1
     5         18               23882              1              387              1
     6         21             2418.33            2.5            6e+03            2.5
     7         24             1421.98        5.08058         1.33e+04           6.25
     8         27             46.4089       0.628623         1.54e+03           6.25
     9         30            0.202457      0.0731742             99.1           6.25
    10         33         5.13306e-07     0.00327404            0.158           6.25
    11         36          4.6841e-17    9.04036e-06         1.51e-06           6.25
    12         39          3.2438e-27    5.02268e-11         1.25e-11           6.25

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.

Plotting graphs of the left sides of the system equations:

Warning: Imaginary parts of complex X and/or Y arguments ignored.

ans = function_handle with value:
    @(x)[3*x(1)*x(2)-x(1)^2-x(2)^2-5;7*x(1)^2*x(2)^2-x(1)^4-x(2)^4-155]

function F = M36
% Correction
%   vvvv
F = @(x) [3*x(1)*x(2) - x(1)^2 - x(2)^2 - 5; 
   7*x(1)^2 * x(2)^2 - x(1)^4 - x(2)^4 - 155];

options = optimoptions('fsolve','Display','iter');
[~,~] = fsolve(F,[-4,0],options);
[~,~] = fsolve(F,[0,4],options);
disp('Plotting graphs of the left sides of the system equations:')

x=-5:0.1:5; 
y1 = (3/2).*x+ sqrt((13/4).*x.^2+5); 

figure
plot(y1,x,'b')
hold on

%Correction
%vv           vv         vv     vv   vv vv 
 y2 = sqrt((x.^4 + 155) ./ (7*x.^2 - y1.^2)); 

%Changed the color of the plot to differentiate
plot(y2,x,'r')
hold off
grid on
legend('Graphic solution');
end

[Maria]

I want to solve a system of nonlinear equations 3*x(1)*x(2) - x(1)^2 - x(2)^2 = 5;

7*x(1)^2 * x(2)^2 - x(1)^4 - x(2)^4 = 155 create a file - m using the extended function fzero, check the solution using the roots function, and also plot solutions

[Walter Roberson]

syms x [1 2]
eqns = [3*x(1)*x(2) - x(1)^2 - x(2)^2 == 5;
        7*x(1)^2 * x(2)^2 - x(1)^4 - x(2)^4 == 155]

eqns = 

sol = solve(eqns)

sol = struct with fields:
    x1: [4×1 sym]
    x2: [4×1 sym]

subs([x1, x2], sol)

ans = 

Answer 1

[Walter Roberson]

F = @(x)[3*x(1)*x(2) - x(1)^2 - x(2)^2 - 5; 
 7*x(1)^2 * x(2)^2 - x(1)^4 - x(2)^4 - 155];